light emitting diodes of inverse spin valvesan external bias is applied on the inverse spin valve....

Hindawi Publishing CorporationResearch Letters in PhysicsVolume 2008, Article ID 434936, 4 pagesdoi:10.1155/2008/434936

Research LetterLight Emitting Diodes of Inverse Spin Valves

X. R. Wang

Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Correspondence should be addressed to X. R. Wang, [email protected]

Received 15 May 2008; Accepted 8 July 2008

Recommended by Yuan Feng

Light emitting diodes made out of inverse spin valves of a ferromagnetic half metal sandwiched between two nonmagnetic metalsare proposed. Based on a giant spin-dependent chemical potential difference created under an external bias, the inverse spin valvesare possible to emit light when electrons with the higher chemical potential flip their spins and become the electrons of the oppositespin with the lower chemical potential. The frequency of this type of light emitting diodes is tunable by the bias.

Copyright © 2008 X. R. Wang. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Most light emitting diodes (LEDs) are made of eithernonmagnetic semiconductors or organic semiconductors.The working principle of an LED is to create a situationwhere electrons occupy higher energy levels and some ofthe lower energy levels are unoccupied so that electrons canmove to those lower energy levels by emitting photons. Oneof the popular ways to achieve this in the conventional LEDsis through a p-n junction where electrons are injected intothe conduction band on one side and holes into the valenceband on the other side (of the junction) when the LED iselectrically biased in the forward direction of the junction. Aslong as an electron and a hole are spatially not too far apart,they can radiatively recombine and emit incoherent narrow-spectrum light. Thus, the emitted light depends largely onthe energy difference between electrons and holes. This isalso why a proper electronic structure is normally requiredfor LED materials. How much the light frequency is tunabledepends on the detail energy band structure of the LEDmaterial. On the other hand, all materials can emit light ifthey are in excited states. The question that we would like toask is whether it is possible to make an LED out of materialsthat are normally not for LEDs. In this letter, we propose aninverse spin valve device in which the chemical potentialsof spin-up (SU) and spin-down (SD) electrons split whenan external bias is applied. The degree of the split is at themagnitude of applied bias, and is due to the spin-dependentelectron transport. Thus the device can emit tunable lightunder an external bias. Interestingly enough, this inverse spinvalve is made out of both nonmagnetic and magnetic metals.Traditionally, one will not relate LEDs with magnetism where

one may be interested in the magnetization reversal [1–6].Furthermore, the emitted light is not sensitive to the particu-lar materials used, and thus it is an LED out of any material.

A conventional spin valve is a layered structure of anonmagnetic spacer sandwiched between two ferromagneticmetals. An inverse spin valve is a layered structure with aferromagnet sandwiched between two nonmagnetic metals.As illustrated in Figure 1(a), M1 and M2 are two non-magnetic metals. To maximize the spin-related chemicalpotential split, the ferromagnetic spacer is chosen to bea half metal (HM) that acts as a conductor to electronsof one spin orientation (spin-up), but as an insulatorto those of the opposite orientation (spin-down). Thenonly SU electrons can pass through the half metal whenan external bias is applied on the inverse spin valve. SDelectrons will be blockaded from the flow through the spacer.Similar to a giant magnetoresistance [7–9] or tunnelingmagnetoresistance [10, 11] device, electron transport of aninverse spin valve is spin-dependent.

The spin-dependent electron transport of an inverse spinvalve leads to spin-dependent Fermi levels in nonmagneticmetals near the nonmagnetic-magnetic interfaces under abias. Consider one inverse spin valve connected to a batteryof voltage V . Let us assume that the electron chemicalpotential in M1 is initially moved up by eV while that ofM2 is kept unchanged [12]. The electron flow diagram isshown in Figure 1(b). M1 and M2 each has two electronreservoirs. One is for SU electrons, and the other is for SDelectrons (denoted by rectangular boxes). SU electrons inM1 can flow into the empty SU electronic states in M2 via

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2 Research Letters in Physics

M1 HM M2

V

(a)

Reservoir ofSU electrons




Battery

II

I

I

I/2 I/2

I/2

I/2

M1 M2

I1 I2

(b)

Δμ1

Δμ2

ΔV

E

EE

M1

M2HM

DOS

DOS

(c)

Figure 1: (a) Schematic illustration of the inverse spin valve. M1 and M2 are nonmagnetic metals. HM is a ferromagnetic half metal. V isthe applied bias. (b) Electron flow from and into spin-up and spin-down states in M1 and M2. In the steady state, current flowing into anyreservoir should be equal to those flowing out. (c) Relative chemical potentials of spin-up and spin-down electrons in nonmagnetic metalsand half metal. The curved arrows indicate the electron flow. Dash lines indicate the chemical potential levels of spin-up and spin-downelectrons in half metal and nonmagnetic metals. Δμ1 and Δμ2 are the chemical potential splits between spin-up and spin-down electrons atthe left and right nonmagnetic-magnetic interfaces. ΔV is the effective bias on the half metal.

the empty SU electronic states in the half metal, generatinga current I from M1 to M2. There is no current betweenthe SD-electron reservoir of M1 and SD-electron reservoirof M2 due to the spin blockade of the half metal. The sameamount of electrons will be pumped back from M2 to M1by the battery to keep the electron neutrality in M1 and M2.However, a battery does not distinguish electron spin, andit pumps equal amounts of SU and SD electrons. In otherwords, SU electrons flow out of M1 and into M2. In themeanwhile, an equal amount of electrons with half of themin the SU state and the other half in the SD state are drawnout of M2 and are supplied into M1 by a battery. As a result,M1 accumulates more SD electrons, and M2 accumulatesmore SU electrons. Thus, the chemical potential of the SDelectrons is higher than that of the SU electrons in M1. Viceversa, the Fermi level of SU electrons is higher than that ofSD electrons inM2. Figure 1(c) is an illustration of the Fermilevels (denoted by the dash lines) of SU and SD electrons in

nonmagnetic metals and half metal. The electron density ofstates (DOSs) in the figure for nonmagnetic metals and halfmetal is just a sketch. Δμ1 and Δμ2 are the chemical potentialdifferences between SU and SD electrons in M1 and M2,respectively. ΔV is the chemical potential difference betweenthe SU electrons in M1 and the SU electrons in M2.

SD electrons in M1 can only go to M2 by first flippingtheir spins and changing to SU electrons. The only supply ofthe SD electrons toM2 is from the conversion of the SU elec-trons in M2 through spin flipping. As shown in Figure 1(b),these lead to the internal currents I1 (I2) in M1 (M2)between SD-electron and SU-electron reservoirs. Assume thespin flip occurs only near nonmagnetic-magnetic interfaceswithin a width of spin diffusion length ξ1 (ξ2) in M1 (M2).This is justified because ξi (i = 1, 2) is the length scaleover which a chemical potential difference can maintain,and the conversion rate of SU and SD electrons from eachother is the same when both SU and SD electrons have

X. R. Wang 3

the same Fermi levels (chemical potentials). Let τ1 (τ2) bethe spin flipping time (spin-relaxation time T1 [13]) inM1 (M2), corresponding to the flipping rate of 1/τ1 (1/τ2).The conversion rate from the SD (SU) electrons to the SU(SD) electrons in M1 (M2) is the product of the excess SD(SU) electrons n1Δμ1ξ1A (n2Δμ2ξ1A) and the single electronflipping rate. Thus Ii (i = 1, 2) is

Ii = niΔμieξiA

τi, (1)

where n1 (n2) is the density of states of the SD electronsin M1 (M2) at the Fermi level. A is the cross-sectionareas.Neglecting the tunneling by the SD electrons throughthe half metal and assuming a resistance R for the SUelectrons, the current I fromM1 toM2 is

I = ΔV

R. (2)

In the steady state, there is no net electron build up anywherein the circuit. Since the current through the battery isunpolarized, half of the current is made up by the SUelectrons and the other half is from the SD electrons. Balanceconditions and external constraint require

I1 = I2 = I

2,

Δμ1

e+Δμ2

e+ ΔV = V.

(3)

Solving (1)–(3), the spin-dependent chemical potentialdifferences Δμ1 and Δμ2 are

Δμ1 = (eV)τ1/(n1e2ξ1A

)

2R + τ1/(n1e2ξ1A

)+ τ2/

(n2e2ξ2A

) ,

Δμ2 = (eV)τ2/(n2e2ξ2A

)

2R + τ1/(n1e2ξ1A

)+ τ2/

(n2e2ξ2A

) .

(4)

It is interesting to see that the largest chemical potential splitsoccur at R = 0, a short circuit for SU electrons! The chemicalpotential splits are largely determined by the applied bias.Thus they could be the order of eV if the steady current(controlled by the relaxation time and bias) is not too largeto cause an electric breakdown. The half metal may alsobe replaced by an ordinary ferromagnet. In this case, SDelectrons in M1 can also flow directly into M2. As long asthere is a spin-dependent electron transportation, the spin-related chemical potential differences in M1 and M2 alwaysexist but their values will be reduced by a factor of (1−R/R′),where R′ is the resistance of the ferromagnet for the SDelectrons (minority carriers).

Results of (4) mean the population inversion of theelectrons in the electrically biased inverse spin valves. Asshown in Figure 2(a) for M1, SU electronic states belowtheir Fermi level are fully occupied (at zero temperature)while the SD electronic states in the energy range of Δμ1

between SU electron Fermi level and SD electron Fermi levelare empty. Thus an SU electron can go to a lower emptySD electronic state and emit a photon. One can then applystandard theory of LED to the inverse spin valve device tomake an LED or even a laser by incorporating the devicewith a cavity [14]. However, unlike the usual light source

ν

Δμ1

(a)

y

x

z

V ν

M1

M2HM

(b)

Figure 2: (a) Schematic illustration of light emitting process inM1. SU electrons near the Fermi level jump to the lower emptySD electronic states, and emit photons of well-defined polarity.(b) A sketch of a possible LED out of an inverse spin valve. Ifthe magnetization of the half metal is along the z-axis, the lightemitted by M1 along the +z-direction will be right-hand circularlypolarized. No light will emit in the xy-plane.

of atoms and semiconductors where spin does not involvein the electron transitions, the light source here is spinresolved. For example, in the case that the magnetization ofthe half metal is along the +z-direction, the spin-up (+z-direction) electrons in M1 are in higher energy levels, andthey can only go to spin-down states. Due to the angularmomentum conservation, the spin of the emitted photonmust be along the +z-direction. In other words, the light outof an inverse spin valve is polarized. Its polarization dependson the light propagation direction and magnetization ofthe half metal. As shown in Figure 2(b), the light emittedin the +z-direction is right-hand circularly polarized light,and left-hand circularly polarized light in the −z-direction.Because of the two-component nature of photons (angularmomentums must be parallel to light propagation direction),no light can emit in the direction perpendicular to themagnetization of the half metal (xy-plane).

It should be clear that electroluminescence in a spin-flip transition does not violate any fundamental principles,such as energy, angular momentum, and linear momentumconservations. The energy and angular momentum conser-vations are satisfied by emitting a photon with a properfrequency and angular momentum. Linear momentum con-servation is easily satisfied, just as all radiative transitions invapors or liquids or solids that can absorb readily any negligi-ble linear momentum of a photon (this is why a good opticalsemiconductor should have a direct band gap). In a normalLED, radiative transitions occur between two states in twodifferent bands with opposite parities. To have a finite dipole-induced electroluminescence, one needs a nonzero dipolematrix element 〈β|−→x |α〉 /= 0, where |α〉 and |β〉 are the initialand finite electronic states (in the same band). Thus, this isonly possible in a metal without inversion symmetry! Thisrequirement is similar to that in a cascade laser [15] of

4 Research Letters in Physics

superlattices. Electroluminescence in a spin-flip transition isalso supported by the fact that magnetization dynamics canbe manipulated by the laser of femtosecond time-scales [16].This fact indicates a strong coupling between photons andelectron spin-flipping. Furthermore, in a conventional semi-conductor, an electron decay within the same energy band isdominated by nonradiative one due to the electron-photoninteraction whose time scale is typically picoseconds in com-parison with nanoseconds for a radiative one. The nonradia-tive decay is expected to be greatly suppressed in our systembecause the direct photon-electron and electron-electroninteractions cannot flip electron spins. Thus, radiative decayfrom occupied SU electron states to empty SD electron statesshould be the favored channel. Of course, nonradiative decayis still possible when the spin-orbital coupling is strong.

In comparison with the usual semiconductor LEDs,there are a few nice features about the proposed LED. (1)Photons have a well-defined polarization because bothoccupied and unoccupied states have well defined spins. (2)The population inversion is not very sensitive to the detailelectronic structure, thus the physics is very robust, andone can in principle use any conducting materials, magneticor nonmagnetic and organic or inorganic, to make LEDs.(3) The spin-dependent chemical potential difference iscontrolled by an external bias, thus the light frequency canbe electrically tuned over very broad range.

Zero temperature is assumed in (1). For a finite tem-perature, electron distribution is no longer described by astep-function, and (1) should be modified. Also, the spatialvariation of the Fermi level is neglected in the present work.In principle, Fermi levels of both SU and SD electrons varyin space because of electron diffusion, spatial distributionof electrons, and spin flipping. The spatial variation of theFermi levels may also modify (1). For practical applications,it is interesting to work out a more careful analysis by takinginto account the electron distribution in both energy andspace although one should not anticipate any change inphysics.

The working principle of currently proposed LED deviceis different from the traditional ones. Unlike many previousLEDs where electron spin degrees of freedom were not used,the LED devices here are largely based on manipulating elec-tron spins through the spin-dependent electron transportin inverse spin valves so that it is possible to create higheroccupied SU (SD) electron levels and lower unoccupiedSD (SU) levels. The population inversion does not occurbetween states of the same spin, but for opposite spin instead.However, it should be pointed out that concept of spin-LEDis not new [17, 18].

In conclusion, we propose a very robust LED devicemade of almost any material. Unlike the usual LEDs thatrely on detail energy spectrum of the material, the proposedtechnology uses electron spin blockage to create a populationinversion of electrons.

ACKNOWLEDGMENTS

The author would like to thank Professor Yongli Gao andProfessor John Xiao for the useful discussions. This work is

supported by Grants no. RPC07/08.SC03, RGC/GRF603508,RGC/CERG603007, and SBI07/08.SC09.

REFERENCES

[1] X. R. Wang and Z. Z. Sun, “Theoretical limit in the magneti-zation reversal of Stoner particles,” Physical Review Letters, vol.98, no. 7, Article ID 077201, 4 pages, 2007.

[2] Z. Z. Sun and X. R. Wang, “Theoretical limit of the minimalmagnetization switching field and the optimal field pulse forStoner particles,” Physical Review Letters, vol. 97, no. 7, ArticleID 077205, 4 pages, 2006.

[3] Z. Z. Sun and X. R. Wang, “Fast magnetization switchingof Stoner particles: a nonlinear dynamics picture,” PhysicalReview B, vol. 71, no. 17, Article ID 174430, 9 pages, 2005.

[4] Z. Z. Sun and X. R. Wang, “Strategy to reduce minimalmagnetization switching field for Stoner particles,” PhysicalReview B, vol. 73, no. 9, Article ID 092416, 4 pages, 2006.

[5] Z. Z. Sun and X. R. Wang, “Magnetization reversal throughsynchronization with a microwave,” Physical Review B, vol. 74,no. 13, Article ID 132401, 4 pages, 2006.

[6] T. Moriyama, R. Cao, J. Q. Xiao, et al., “Microwave-assistedmagnetization switching of Ni80Fe20 in magnetic tunneljunctions,” Applied Physics Letters, vol. 90, no. 15, Article ID152503, 3 pages, 2007.

[7] M. N. Baibich, J. M. Broto, A. Fert, et al., “Giant magnetore-sistance of (001)Fe/(001)Cr magnetic superlattices,” PhysicalReview Letters, vol. 61, no. 21, pp. 2472–2475, 1988.

[8] G. Binach, P. Grunberg, F. Saurenbach, and W. Zinn,“Enhanced magnetoresistance in layered magnetic structureswith antiferromagnetic interlayer exchange,” Physical ReviewB, vol. 39, no. 7, pp. 4828–4830, 1989.

[9] R. F. C. Farrow, C. H. Lee, and S. S. P. Parkin, “Magnetic mul-tilayer structures,” IBM Journal of Research and Development,vol. 34, no. 6, pp. 903–915, 1990.

[10] T. Miyazaki and N. Tezuka, “Giant magnetic tunneling effectin Fe/Al2O3/Fe junction,” Journal of Magnetism and MagneticMaterials, vol. 139, no. 3, pp. L231–L234, 1995.

[11] J. S. Moodera, L. R. Kinder, T. M. Wong, and R. Meservey,“Large magnetoresistance at room temperature in ferromag-netic thin film tunnel junctions,” Physical Review Letters, vol.74, no. 16, pp. 3273–3276, 1995.

[12] S. D. Wang, Z. Z. Sun, N. Cue, H. Q. Xu, and X. R. Wang,“Negative differential capacitance of quantum dots,” PhysicalReview B, vol. 65, no. 12, Article ID 125307, 4 pages, 2002.

[13] X. R. Wang, Y. S. Zheng, and S. Yin, “Spin relaxation anddecoherence of two-level systems,” Physical Review B, vol. 72,no. 12, Article ID 121303, 4 pages, 2005.

[14] H. Haken, Laser Theory, Springer, New York, NY, USA, 1983.[15] F. Capasso, Physics of Quantum Electron Devices, Springer, New

York, NY, USA, 1990.[16] A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M.

Balbashov, and Th. Rasing, “Ultrafast non-thermal controlof magnetization by instantaneous photomagnetic pulses,”Nature, vol. 435, no. 7042, pp. 655–657, 2005.

[17] R. Fiederling, M. Keim, G. Reuscher, et al., “Injection anddetection of a spin-polarized current in a light-emittingdiode,” Nature, vol. 402, no. 6763, pp. 787–790, 1999.

[18] A. T. Hanbicki, B. T. Jonker, G. Itskos, G. Kioseoglou, andA. Petrou, “Efficient electrical spin injection from a magneticmetal/tunnel barrier contact into a semiconductor,” AppliedPhysics Letters, vol. 80, no. 7, pp. 1240–1242, 2002.

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light emitting diodes of inverse spin valvesan external bias is applied on the inverse spin valve....

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